Smooth Tests of Copula Specification under General Censorship

We propose a family of smooth tests of copula specification of multivariate copula models under general censorship. We consider both parametric and semiparametric testing procedures. We establish the large sample properties of both approaches. Our Monte Carlo simulations show that the parametric tests, when correctly specified, perform well but are sensitive to mis-specification of the marginal distributions. The semiparametric tests provide satisfactory overall performance, which is comparable to and sometimes superior to that of correctly-specified parametric tests. Our tests are distribution free and provide guidance on alternative copula specifications when the null hypothesis is rejected. We illustrate the usefulness of the proposed tests in two empirical applications